I own the galaxy S III and I'm very happy with it. With the GS3 and One X you would probably be happy with either as they are both very solid phones. Display wise, the One X's lcd2 display offers whiter whites while the GS3 AMOLED display offers incredibility dark blacks. The GS3 general has better battery life than the One X and also you can pick up a second battery for $20 if you need extra battery life from it having a removable battery. Also GS3 has a major advantage when it comes to storage with it having a microsd slot. I got a 64gb microsd card with mine (Amazon $50) and now I have 80 GB of storage on my phone!

The LG Optimus G looks very promising but I would recommended waiting a month or 2 before picking up so you can get user reviews from people who actually use it in their lives for over a month. It is rumored and pretty much a fact with amount of leaks that the next Nexus device is going to be based on the Optimus G design. If you care about having faster updates for your phone you might want to wait a month for it to come out (Google is anounceing it on Oct 29th).

I would also suggest looking at the new Motorola RAZR maxx HD as it looks very good or on par with all the other top of the line Android phones. It also looks to have the best battery life out of any phone.